Having bone animation problem!
Both of your arms appear to be weighted to the left arm bones. In fact it appears that you don't have any right arm bones.

If you are using a mirror modifier, make sure mirror vertex weights is checked on the modifier panel.

Create your right arm bones and make sure all the left arm bones and right arm bones follow blender's mirror naming convention (names should match appart from a .L or .R suffix depending on whether they are left or right). 

Delete all vertex weights on you model and remove the armature modifier from the mesh. Then reparent the mesh to the armature with automatic weights.

Alternatively, you can select all the vertices on the right arm, and remove them from each of the left arm vertex groups using the button in the vertex groups section of the mesh properties panel.